Based on your score and since your category is general , there are very few chances of getting any old IIT and top NITs.  You can try for new IITs and some low ranking NITs. If you want to take a good IIT or NIT then you have to compromise with your branch. One thing i would like to mention here that some of the IITs conduct interview and written examination for selection. So sit for that, if you will perform well then there are chances of getting IITs.

There are other departments also which consider GATE ME paper apart from mechanical like thermal engineering , machine design,etc.

Few institutes like :

IITs: Guwahati, BHU, Bhubaneswar,etc.

NITs: Jaipur, Agartala, Surat, Patna, Calicut, Durgapur , Raipur Srinagar,etc.

There are other private institutes also where you can try.

If you are a final year student, then you can drop a year and try next year.